General Information
Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Logic and Discrete Theory
Date Adopted or Revised: 08/20
Status: State Board Approved
Benchmark Instructional Guide
Connecting Benchmarks/Horizontal Alignment
Terms from the K-12 Glossary
Vertical Alignment
Previous Benchmarks
Next Benchmarks
Purpose and Instructional Strategies
In Math for College Liberal Arts students will learn to perform set operations including complement, union, intersection, difference and product of two sets. In later classes, students will continue working with these operations.- Instruction includes connection to MA.912.LT.5.5 and using Venn Diagrams to help students visualize set operations.
- Instruction includes discussion of a universal set U which contains all the possible elements of a set.
- Instruction includes finding the complement of a set denoted by the word NOT. The
complement of a set A is all elements in the universal set that are not in the set A. The
complement is written A′. Other benchmarks may refer to the complement set as Ac ,-A-, A′ or ~A.
- Example:
- Given U = {1,2,3,4,5,6,7} and A = {2,4,6}, A′ = {1,3,5,7}.
- Example:
- Instruction includes finding the union of two sets denoted by the word OR. The union of
sets A and B is the set of all elements in set A OR in set B OR in both sets. The union of
sets A and B is written A ∪ B.
- Example:
- Given A = {1,2,3,4,5} and B = {2,4,6,8}, A ∪ B = {1,2,3,4,5,6,8}.
- Example:
- Instruction includes finding the intersection of two sets denoted by the word AND. The
intersection of sets A and B is the set of all elements in both set A AND set B. The
intersection of sets A and B is written A ∩ B.
- Example:
- Given A = {1,2,3,4,5} and A = {2,4,6,8}, A ∩ B = {2,4}.
- Example:
- Instruction includes finding the difference of two sets. The difference between sets A and B is the set of all elements in set A that are not in set B. The difference of sets A and B is
written A − B. Note that order is important when finding a difference.
- Example:
- Given A = {1,2,3,4,5} and B = {2,4,6,8}, A − B = {1,3,5}.
- Example:
- Given A = {1,2,3,4,5} and B = {2,4,6,8}, B − A = {6,8}.
- Example:
- Instruction includes finding the product of two sets. The product of sets A and B is the set
of ordered pairs (a, b) where a is an element of set A and b is an element of set B. The
product of sets is sometimes called the Cartesian product or cross product. The product of
sets A and B is written A × B. Note that order is important when finding a product.
- Example:
- Given A = {a, b} and B = {1,2,3}, A × B = {(a, 1), (a, 2), (a, 3), (b, 1), (b, 2), (b, 3)}
- The product can be demonstrated in table form.
- Example:
- Example:
- Given A = {a, b} and B = {1,2,3}, B × A = {(1, a), (1, b), (2, a), (2, b), (3, a), (3, b)}
- Instruction makes the connection between set operations and probability.
Common Misconceptions or Errors
- Students may repeat elements that are in both sets when writing the union.
- Students may confuse union and intersection.
- Students may incorrectly apply the word “and” when applying set operations.
Instructional Tasks
Instructional Task 1 (MTR.2.1)- Given U is the set of letters of the alphabet, A is the set of vowels and B is the set of letters that come before k, describe the following in words and then write the resulting sets in roster form:
a. A′
b. B′
c. A ∪ B
d. A ∩ B
e. A − B
f. B − A
Instructional Task 2 (MTR.2.1)
- Given set A is the set of even numbers less than or equal to six and set B is the set of odd numbers greater than 4 and less than 8, write the following sets in roster form.
a. A
b. B
c. A × B
d. B × A
e. A − B
f. B − A
Instructional Items
Instructional Item 1- Given A = {1,3,5,7,9} and B = {1,2,3,4,5}, find A ∩ B.
- Given the sets:
A = {2, 5, 8, 9, 11, 13}
B = {1, 2, 3, 4, 5, 9, 10}
- Find the following:
- A U B
- A ∩ B
- A ∩ B′